%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET626+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 05:27:37 EDT 2022

% Result   : Theorem 0.18s 0.41s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   7 unt;   0 nHn;  12 RR)
%            Number of literals    :   18 (   0 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ intersect(skc3,skc4),
    file('SET626+3.p',unknown),
    [] ).

cnf(2,axiom,
    intersect(skc3,intersection(skc4,skc5)),
    file('SET626+3.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,v) ),
    file('SET626+3.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ intersect(u,v)
    | member(skf2(v,u),u) ),
    file('SET626+3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ intersect(u,v)
    | member(skf2(v,w),v) ),
    file('SET626+3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ member(u,v)
    | ~ member(u,w)
    | intersect(w,v) ),
    file('SET626+3.p',unknown),
    [] ).

cnf(16,plain,
    ( ~ member(u,skc4)
    | ~ member(u,skc3) ),
    inference(res,[status(thm),theory(equality)],[9,1]),
    [iquote('0:Res:9.2,1.0')] ).

cnf(27,plain,
    member(skf2(intersection(skc4,skc5),u),intersection(skc4,skc5)),
    inference(res,[status(thm),theory(equality)],[2,8]),
    [iquote('0:Res:2.0,8.0')] ).

cnf(36,plain,
    member(skf2(intersection(skc4,skc5),u),skc4),
    inference(res,[status(thm),theory(equality)],[27,5]),
    [iquote('0:Res:27.0,5.0')] ).

cnf(41,plain,
    ~ member(skf2(intersection(skc4,skc5),u),skc3),
    inference(res,[status(thm),theory(equality)],[36,16]),
    [iquote('0:Res:36.0,16.0')] ).

cnf(43,plain,
    ~ intersect(skc3,intersection(skc4,skc5)),
    inference(res,[status(thm),theory(equality)],[7,41]),
    [iquote('0:Res:7.1,41.0')] ).

cnf(44,plain,
    $false,
    inference(mrr,[status(thm)],[43,2]),
    [iquote('0:MRR:43.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SET626+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n004.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jul 11 08:48:07 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.41  
% 0.18/0.41  SPASS V 3.9 
% 0.18/0.41  SPASS beiseite: Proof found.
% 0.18/0.41  % SZS status Theorem
% 0.18/0.41  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.41  SPASS derived 27 clauses, backtracked 0 clauses, performed 0 splits and kept 30 clauses.
% 0.18/0.41  SPASS allocated 85298 KBytes.
% 0.18/0.41  SPASS spent	0:00:00.07 on the problem.
% 0.18/0.41  		0:00:00.03 for the input.
% 0.18/0.41  		0:00:00.02 for the FLOTTER CNF translation.
% 0.18/0.41  		0:00:00.00 for inferences.
% 0.18/0.41  		0:00:00.00 for the backtracking.
% 0.18/0.41  		0:00:00.00 for the reduction.
% 0.18/0.41  
% 0.18/0.41  
% 0.18/0.41  Here is a proof with depth 4, length 12 :
% 0.18/0.41  % SZS output start Refutation
% See solution above
% 0.18/0.41  Formulae used in the proof : prove_th102 intersection_defn intersect_defn
% 0.18/0.41  
%------------------------------------------------------------------------------